In this work, we are interested in capacities which are deformations of probability i.e v = f ◦ P . We characterize balanced, totally balanced, exact and convex capacities, by properties concerning the probability transformation function, f . We also give the explicit expression, in the case of a convex capacity v = f ◦ P , of a probability in the core of v which coincides with v on a given fin...

Geometric and stochastic representations are derived for the big class of p-generalized elliptically contoured distributions, and (generalizing Cavalieri?s and Torricelli?s method of indivisibles in a non-Euclidean sense) a geometric disintegration method is established for deriving even more general star-shaped distributions. Applications to constructing non-concentric elliptically contoured a...

We report a new type of standing gravity wave of large amplitude, having alternatively the shape of a star and of a polygon. This wave is observed by means of a laboratory experiment by vertically vibrating a tank. The symmetry of the star (i.e., the number of branches) is independent of the container form and size, and can be changed according to the amplitude and frequency of the vibration. W...

Lévy particles provide a flexible framework for modelling and simulating threedimensional star-shaped random sets. The radial function of a Lévy particle arises from a kernel smoothing of a Lévy basis, and is associated with an isotropic random field on the sphere. If the kernel is proportional to a von Mises–Fisher density, or uniform on a spherical cap, the correlation function of the associa...

The paper presents a computation-oriented method for characterizing and obtaining local control Lyapunov functions induced by particular star-shaped nonconvex sets for continuous-time nonlinear systems with bounded inputs. For a given set, the necessary and sufficient conditions for the induced function to be a nonconvex local control Lyapunov function are provided. The related convex problems ...

We have derived large-scale dust column density maps for a complete set of nearby molecular clouds using a near-infrared extinction mapping technique. With these data, we performed the first systematic study of column density probability distributions in molecular clouds. We found that the probability density functions (PDFs) of non-star-forming clouds are almost always well-fitted by lognormal...